Given:
[tex]-2x^3-16y^3[/tex]Aim:
We need to factorize the given polynomial.
Explanation:
Take out the common term (-2).
[tex]-2x^3-16y^3=-2(x^3+8y^3)[/tex][tex]\text{Use }8=2^3.[/tex][tex]-2x^3-16y^3=-2(x^3+2^3y^3)[/tex][tex]-2x^3-16y^3=-2(x^3+(2y)^3)[/tex][tex]\text{ Use }a^3+b^3=(a+b_{})(a^2-ab+b^2),\text{ Here a=x and b=2y.}[/tex][tex]-2x^3-16y^3=-2(x+y_{})(x^2-xy+y^2)[/tex]Final answer:
[tex]-2(x+y_{})(x^2-xy+y^2)[/tex]